can be rearranged to this near-equivalent matrix (resistors have been relocated). This emphasizes the similarities between ordinary grid multiplex and Charlieplex, and demonstrates the pattern that leads to "the n-squared minus n" rule. In typical usage on a circuit board the resistors would be physically located at the top of the columns and connected to the input pin. The rows would then be connected directly to the input pin bypassing the resistor. The first setup in the image on the left is suitable only when identical LEDs are used since a single resistor is used for current-limiting through more than one LED (though not at the same time—rather, one resistor limits current through only one LED in a given column at one time). This is contrasted to the second configuration with individual resistors for each LED, as shown in the image on the right. In this second configuration, each LED has a unique resistor paired with it. This makes it possible to mix different kinds of LEDs by providing each with its appropriate resistor value. In both of these configuration, as shown in both the left and the right image, the relocated resistors make it possible to light multiple LEDs at the same time row-by-row, instead of requiring that they be lit individually. The row current capacity could be boosted by an NPN emitter follower BJT transistor instead of driving the current directly with the typically much weaker I/O pin alone. Problems with Charlieplexing Refresh rate Because only a single set of LEDs, all having a common anode or cathode, can be lit simultaneously without turning on unintended LEDs, Charlieplexing requires frequent output changes, through a method known as multiplexing. When multiplexing is done, not all LEDs are lit quite simultaneously, but rather one set of LEDs is lit briefly, then another set, and eventually the cycle repeats. If it is done fast enough, they will appear to all be on, all the time, to the human eye because of persistence of vision. In order for a display to not have any noticeable flicker, the refresh rate for each LED must be greater than 50 Hz. Suppose 8 tri-state pins are used to control 56 LEDs through Charlieplexing, which is enough for 8 7-segment displays (without decimal points). Typically 7-segment displays are made to have a common cathode, sometimes a common anode, but without loss of generality suppose it is